Gravitational-wave standard sirens present a novel approach for the determination of the Hubble constant. After the recent spectacular confirmation of the method thanks to GW170817 and its optical counterpart, additional standard siren measurements from future gravitational-wave sources are expected to constrain the Hubble constant to high accuracy. At the same time, improved constraints are expected from observations of cosmic microwave background (CMB) polarization and from baryon acoustic oscillation (BAO) surveys. We explore the role of future standard siren constraints on $H_0$ in light of expected $\mathrm{CMB}+\mathrm{BAO}$ data. Considering a ten-parameter cosmological model, in which curvature, the dark energy equation of state, and the Hubble constant are unbounded by CMB observations, we find that a combination of future $\mathrm{CMB}+\mathrm{BAO}$ data will constrain the Hubble parameter to $\sim 1.5\%$. Further extending the parameter space to a time-varying dark energy equation of state, we find that future $\mathrm{CMB}+\mathrm{BAO}$ constraints on $H_0$ are relaxed to $\sim 3.0\%$. These accuracies are within reach of future standard siren measurements from the Hanford-Livingston-Virgo and the Hanford-Livingston-Virgo-Japan-India networks of interferometers, showing the cosmological relevance of these sources. If future gravitational-wave standard siren measurements reach 1% on $H_0$, as expected, they would significantly improve future $\mathrm{CMB}+\mathrm{BAO}$ constraints on curvature and on the dark energy equation of state by up to a factor of $\sim 3$. We also show that the inclusion of $H_0$ constraints from gravitational-wave standard sirens could result in a reduction of the dark energy figure of merit (i.e., the cosmological parameter volume) by up to a factor of $\sim 400$.

• Received 23 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.083523